If the scaling factor of DEF with respect to D'E'F' is 3, determine the length of the

If the scaling factor of ΔDEF with respect to ΔD'E'F' is 3, determine the length of the sides of triangle ΔD'E'F'.

We use a scaling factor. Examine the similar triangles ABC and A'B'C' in the figure below.

If we calculate the ratios AB/A'B', BC/B'C', and CA/C'A', we see that each of these ratios is equal to 2. We call this common ratio the scaling factor of ΔABC with respect to ΔA'B'C'. If we calculate the reciprocal ratios A'B'/AB, B'C'/BC, and C'A'/CA, we see that each of these ratios is equal to 1/2. We call this common ratio the scaling factor of ΔA'B'C' with respect to ΔABC. Every pair of similar figures has two scaling factors that show the relationship between the corresponding side lengths.

Transcribed Image Text:

D' 12 F' `E' 15 10 A'r 5 3 B C' 4 B'